Digital halftoning, also referred to as spatial dithering, is a process in which digital input signals to a digital printer are modified prior to printing a hard copy, such that a digitally printed version of a photographic image creates the illusion of the continuous tone scale of the photographic original. Most hard copy devices such as ink-jet printers and laser printers, whether write-black, write-white, or in color, operate in a binary mode, i.e. a printed dot is either present or absent on a two-dimensional printer medium at a specified location. Thus, due to the binary nature of such printers, a true continuous tone reproduction of a photographic image is not possible with digital printers. However, in order to approach the appearance of continuous tone, the digital input signals to the printer are modified prior to printing so as to direct the printer to spatially distribute fewer or more printed dots in the neighborhood or vicinity of a designated dot, thereby increasing or decreasing the distribution of printed dots about a designated area on the print. Since different types of printers, and even different printers among the same printer type, produce differently sized and differently shaped printed dots, and since even a chosen digital printer frequently generates printed dots having a size variation as a function of dot position, it has become apparent that a halftone correction system must be tailored to the characteristics of a particular chosen digital printer. Frequently, printed dots from write-black printers and write-white printers are of a size and shape such that dots printed adjacent to each other tend to overlap. Accordingly, a successful halftone correction system has to include considerations related to dot overlap correction. In a recent publication, titled Measurement of Printer Parameters for Model-based Halftoning, T. N. Pappas, C. K. Dong, and D. L. Neuhoff, Journal of Electronic Imaging, Vol. 2 (3), pages 193-204, July 1993, there are described various approaches toward halftone correction based on a dot overlap model of dots printed by a particular digital printer. To accomplish halftone correction, Pappas, et al. describe printing of a variety of test patterns by the same printer. The test patterns are intended to be used for characterization of printed dot overlap and are measured by a reflection densitometer (see particularly pages 198 and 199 of the Pappas, et al. publication) so as to obtain measured values of average reflectance of these various test patterns. The calculated printer model parameters, based on the measurement of test patterns, are then used to provide halftone correction or gray scale rendition of digital image data representative of an original image to be printed. Halftone correction can be accomplished for example by a known so-called modified error diffusion algorithm or by a known least-squares model algorithm. In the overlap correction approach described by Pappas et al., each printed dot is positioned within a superimposed or overlaid virtual Cartesian grid such that the center of each dot is coincident with the center of the spacing between adjacent grid lines. Accordingly, Pappas, et al. require at least 32 total test patterns for the simplest shape of the scanning window, 512 possible test patterns for a 3.times.3 scanning virtual window, and a total of 33,554,432 possible test patterns for a 5.times.5 scanning virtual window matrix. Even when considering that dot overlapping can be symmetric about both the x and y directions of the grid, thereby reducing the number of possible patterns, the computational complexity and associated complicated optimization calculations become formidable in the overlap correction approach described by Pappas, et al.
Another publication, titled Measurement-based Evaluation of a Printer Dot Model for Halftone Algorithm Tone Correction, by C. J. Rosenberg, Journal of Electronic Imaging, Vol. 2 (3), pages 205-212, July 1993, describes a tone scale correction approach for digital printers which produce potentially overlapping circular dots, each dot centered at the center of a grid opening of a superimposed grid. This dot overlapping model assumes that all printed dots have a perfectly circular shape. Here, the reflectance of a number of constant gray scale test patches or test patterns is measured, and the reflectance values are inverted to obtain a correction curve. This measurement-based calibration of a printer (see FIG. 2 of the Rosenberg paper) is repeated for all digital gray levels anticipated to be printed by the printer. The tone response correction curves are then used in conjunction with one of several known halftoning algorithms to generate a calculated dot diameter which would provide a best fit to the measured data, whereby one best fit approach is based on minimizing the rms error between the measured tone response curve and that derived from the model, and a second approach is based on generating an improved match in terms of the visual perception by a human observer.
Thus, digital halftone correction and particularly dot overlapping halftone correction relies upon the determination of the actual physical output of a printer for given binary digital printer input signals. Accordingly, it would be desirable to devise a halftone correction system for overlapping printed dots which minimizes the required number of test patterns, thereby minimizing the complexity of determinations of the extent of printed dot overlap and the attendant computations, while achieving an effective dot-overlapping halftone correction system.